A moment map for the G-action on (M, ω) is a map such that
for all ξ in . Here is the function from M to R defined by . The moment map is uniquely defined up to an additive constant of integration.
A moment map is often also required to be G-equivariant, where G acts on via the coadjoint action. If the group is compact or semisimple, then the constant of integration can always be chosen to make the moment map coadjoint equivariant; however in general the coadjoint action must be modified to make the map equivariant (this is the case for example for the Euclidean group).
Read more about Moment Map: Hamiltonian Group Actions, Examples, Symplectic Quotients
Famous quotes containing the words moment and/or map:
“The next moment he was “showing off” with all his might—cuffing boys, pulling hair, making faces—in a word, using every art that seemed likely to fascinate a girl and win her applause.”
—Mark Twain [Samuel Langhorne Clemens] (1835–1910)
“The Management Area of Cherokee
National Forest, interested in fish,
Has mapped Tellico and Bald Rivers
And North River, with the tributaries
Brookshire Branch and Sugar Cove Creed:
A fishy map for facile fishery....”
—Allen Tate (1899–1979)